High School

Which choice is equivalent to the expression below?

[tex]\sqrt{32} - \sqrt{2}[/tex]

A. [tex]16 \sqrt{2}[/tex]
B. [tex]\sqrt{30}[/tex]
C. [tex]3 \sqrt{2}[/tex]
D. 4

Answer :

To solve the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex], we'll simplify it step by step:

1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- We can rewrite 32 as [tex]\(16 \times 2\)[/tex].
- Thus, [tex]\(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{16} = 4\)[/tex], we have [tex]\(\sqrt{32} = 4\sqrt{2}\)[/tex].

2. Subtract [tex]\(\sqrt{2}\)[/tex] from [tex]\(\sqrt{32}\)[/tex]:
- Now, substitute back into the expression: [tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
- Factor out [tex]\(\sqrt{2}\)[/tex]: [tex]\((4 - 1)\sqrt{2}\)[/tex].
- Simplify: [tex]\(3\sqrt{2}\)[/tex].

3. Conclusion:
- The expression simplifies to [tex]\(3\sqrt{2}\)[/tex].

Therefore, the choice that is equivalent to the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] is:

C. [tex]\(3\sqrt{2}\)[/tex]